Ttdfjt

In TikZ, I want to draw two segments (black) and a dashed trajectory (red) encircling these segments, as shown in the picture. Is there a way to easily draw the dashed trajectory just based on the coordinates of the two segments?

Here is my attempt:

begintikzpicture
draw [thick] (1,1) -- (2,2);
draw [thick] (2,2) -- (2,3.5);
draw [dashed] (2.2,2) -- (2.2,3.7) -- (1.8,3.7) -- (1.8,2) -- (0.8,1) -- (1.1,0.8) -- (2.2,2);
endtikzpicture

It doesn't look very nice, and I wasn't able to make the curve.

If you could accept not being dashed, a round cap can help:

documentclass[tikz, border=2mm]standalone

begindocument
begintikzpicture
draw [thick] (1,1) -- (2,2);
draw [thick] (2,2) -- (2,3.5);
draw [dashed] (2.2,2) -- (2.2,3.7) -- (1.8,3.7) -- (1.8,2) -- (0.8,1) -- (1.1,0.8) -- (2.2,2);

beginscope[xshift=2cm]
draw[line cap=round, red!30, line width=2.5mm] (1,1)--(2,2)--(2,3.5);
draw (1,1)--(2,2)--(2,3.5);
endscope

beginscope[xshift=4cm]
draw[line cap=round, line width=3mm] (1,1)--(2,2)--(2,3.5);
draw[line cap=round, white, line width=2.5mm] (1,1)--(2,2)--(2,3.5);
draw (1,1)--(2,2)--(2,3.5);
endscope
endtikzpicture
enddocument

Update: with some patience and hobby library you could do something like:

documentclass[tikz, border=2mm]standalone
usetikzlibraryhobby

begindocument
begintikzpicture
draw (1,1) node (a) --(2,2) node (b) --(2,3.5) node[rotate=45] (c) ;
draw[dashed, use Hobby shortcut] (a.south west) to[closed, curve through=(a.north west) .. (b.north west) .. (c.north west) .. (c.north east) .. (c.south east) .. (b.south east) .. (a.south east)] cycle; 
endtikzpicture
enddocument

The following draws halos around simple paths as the one above. You only need to record the path

draw[thick,postaction=record path=step=5pt] (1,1) -- (2,2) -- (2,3.5);

and then can draw a halo via

draw[dashed,halo];

documentclass[tikz,border=3.14mm]standalone
usetikzlibrarydecorations.markings
newcounterhalo
tikzsetrecord path/.style=/utils/exec=tikzsethalo pars/.cd,#1,
 decorate,decoration=markings,mark=at position 0 with
 setcounterhalo1%typeoutpgfdecoratedpathlength
 path (0pt,pgfkeysvalueof/tikz/halo pars/dist) coordinate (halo-L-numbervaluehalo)
 (0pt,-1*pgfkeysvalueof/tikz/halo pars/dist) coordinate (halo-R-numbervaluehalo)
 (-pgfkeysvalueof/tikz/halo pars/dist/sqrt(2),-pgfkeysvalueof/tikz/halo pars/dist/sqrt(2)) coordinate (halo-A-1)
 (-pgfkeysvalueof/tikz/halo pars/dist,0pt) coordinate (halo-A-2)
 (-pgfkeysvalueof/tikz/halo pars/dist/sqrt(2),pgfkeysvalueof/tikz/halo pars/dist/sqrt(2)) coordinate (halo-A-3);
 pgfmathsetmacromystep(pgfdecoratedpathlength-2*pgfkeysvalueof/tikz/halo pars/step)/int(1+(pgfdecoratedpathlength-2*pgfkeysvalueof/tikz/halo pars/step)/pgfkeysvalueof/tikz/halo pars/step)
 xdefmystepmystep,
 mark=between positions pgfkeysvalueof/tikz/halo pars/step and pgfdecoratedpathlength-pgfkeysvalueof/tikz/halo pars/step step mystep pt with stepcounterhalo
 path (0pt,pgfkeysvalueof/tikz/halo pars/dist) coordinate (halo-L-numbervaluehalo)
 (0pt,-1*pgfkeysvalueof/tikz/halo pars/dist) coordinate (halo-R-numbervaluehalo);,
 mark=at position 1 with stepcounterhalo
 path (0pt,pgfkeysvalueof/tikz/halo pars/dist) coordinate (halo-L-numbervaluehalo)
 (0pt,-1*pgfkeysvalueof/tikz/halo pars/dist) coordinate (halo-R-numbervaluehalo)
 (pgfkeysvalueof/tikz/halo pars/dist/sqrt(2),pgfkeysvalueof/tikz/halo pars/dist/sqrt(2)) coordinate (halo-B-1)
 (pgfkeysvalueof/tikz/halo pars/dist,0pt) coordinate (halo-B-2)
 (pgfkeysvalueof/tikz/halo pars/dist/sqrt(2),-pgfkeysvalueof/tikz/halo pars/dist/sqrt(2)) coordinate (halo-B-3);
 xdefLstHaloCoords(halo-A-1) (halo-A-2) (halo-A-3)
 foreach XX in 1,...,numbervaluehalo
 xdefLstHaloCoordsLstHaloCoordsspace (halo-L-XX)
 xdefLstHaloCoordsLstHaloCoordsspace (halo-B-1) (halo-B-2) (halo-B-3)
 foreach XX in numbervaluehalo,thenumexprnumbervaluehalo-1,...,1
 xdefLstHaloCoordsLstHaloCoordsspace (halo-R-XX)
 ,
 halo/.style=insert path=plot[smooth,samples at=1,...,numbervaluebracep,variable=x]
 (bracep-x),halo/.style=insert path=plot[smooth cycle] coordinates LstHaloCoords ,
 halo pars/.cd,dist/.initial=5pt,step/.initial=2pt
begindocument
begintikzpicture
 draw[thick,postaction=record path=step=5pt] (1,1) -- (2,2) -- (2,3.5);
 draw[dashed,halo];
endtikzpicture
enddocument

The halo path is known to TikZ so it can be used for all sorts of things like intersections or fill with pattern (needs the libraries intersections or patterns), e.g.

draw[thick,postaction=record path=step=5pt] (1,1) -- (2,2) -- (2,3.5);
draw[red,pattern=north west lines,pattern color=blue,halo];

As you can see, the result is not perfect, but can be improved by playing with the step parameter (I chose this on purpose in order not to deceive users). An automatically nice solution that works with much more complicated, in particular self-intersecting, paths is much harder to obtain. However, the above works with curves, too, i.e. not just with straight lines.

Note also that if I only take your dashed contour, add rounded corners and replace the last coordinate by cycle (so that the last corner is also rounded), I get

documentclass[tikz,border=3.14mm]standalone
begindocument
begintikzpicture
draw [thick] (1,1) -- (2,2);
draw [thick] (2,2) -- (2,3.5);
draw [dashed,rounded corners] (2.2,2) -- (2.2,3.7) -- (1.8,3.7) -- (1.8,2) --
(0.8,1) -- (1.1,0.8) -- cycle;
endtikzpicture
enddocument

Things look arguably even better if one draws the fist line in one stretch and takes into account the slope of the lower leg when drawing the contour.

documentclass[tikz,border=3.14mm]standalone
begindocument
begintikzpicture
draw [thick] (1,1) -- (2,2) -- (2,3.5);
draw [dashed,rounded corners] (2.2,1.9) -- (2.2,3.7) -- (1.8,3.7) -- (1.8,2.1) --
(0.8,1) -- (1.1,0.8) -- cycle;
endtikzpicture
enddocument

If you want the dash pattern to close, use

documentclass[tikz,border=3.14mm]standalone
usetikzlibrarydecorations.markings
begindocument
begintikzpicture
draw [thick] (1,1) -- (2,2) -- (2,3.5);
path [rounded corners,preaction=decorate,decoration=markings,mark=at position 0 with %
pgfmathsetmacromyonpgfdecoratedpathlength/50
xdefmyonmyon,postaction=draw,dash pattern=on myon pt off myon pt] (2.2,1.9) -- (2.2,3.7) -- (1.8,3.7) -- (1.8,2.1) --
(0.8,1) -- (1.1,0.8) -- cycle;
endtikzpicture
enddocument